Income taxes - Reconciliation of the Provision (Benefit) for Income Taxes (Details) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Income Tax Disclosure [Abstract]
United States statutory income tax provision (benefit)	$ (57.1)	$ (12.7)	$ 14.9
Income and losses for which no provision or benefit has been recognized	78.6	23.9	19.1
Foreign rate differential and other foreign tax expense	5.9	3.2	9.5
Income tax withholdings	16.8	17.6	19.3
Permanent items	0.8	(2.5)	(5.0)
Enacted rate changes	(4.0)	0.5	(2.3)
Change in uncertain tax positions	3.6	0.2	(1.2)
Change in valuation allowances due to changes in judgment	2.9	(2.3)	(5.9)
Income tax credits, U.S.	(2.1)	(0.2)	(2.4)
Total provision for income taxes	$ 45.4	$ 27.7	$ 46.0